Week 2 content of chess bot
After setting up our chess environment last week, it's time to get started with a simple chess algorithm, minimax. This algorithm forms the foundation of traditional chess engines and will help your bot make intelligent decisions by thinking several moves ahead.
This week, we'll implement a minimax algorithm and learn about how we can make it better through alpha-beta pruning. You'll learn how to make your bot:
- Evaluate chess positions
- Look ahead multiple moves
- Make strategic decisions based on future possibilities
- Understand how to optimize tree search
Minimax is a decision-making algorithm that simulates how two opponents might play a perfect game. It works by:
- Maximizing your chances of winning while
- Minimizing your opponent's chances of winning
1. Look Ahead
- The algorithm creates a tree of possible future moves
- Each level alternates between your moves (maximizing) and opponent's moves (minimizing)
- The depth of this tree is limited by computational resources
2. Evaluate Positions
- At the bottom of the tree, positions are evaluated
- Common factors in evaluation:
- Material count (pawns=1, knights/bishops=3, rooks=5, queens=9)
- Piece positioning (control of center, advanced pawns)
- King safety (pawn shield, castling)
- Mobility (number of legal moves)
3. Backtrack Values
- Values propagate up the tree
- On your turns, pick the maximum value (best for you)
- On opponent's turns, assume they pick the minimum value (worst for you)
## Basic Minimax Implementation
Here's a basic implementation of minimax for your chess bot:
class ChessBot:
def evaluate_position(self, board):
"""
Evaluate the current position.
Positive values favor white, negative values favor black.
"""
if board.is_game_over():
if board.is_checkmate():
return -10000 if board.turn else 10000
return 0 # Draw
score = 0
piece_values = {
'P': 100, 'N': 320, 'B': 330,
'R': 500, 'Q': 900, 'K': 20000
}
# Count material
for piece in piece_values:
score += len(board.pieces(piece, True)) * piece_values[piece]
score -= len(board.pieces(piece, False)) * piece_values[piece]
return score
def minimax(self, board, depth, maximizing_player):
"""
Minimax implementation.
Returns (best_score, best_move)
"""
if depth == 0 or board.is_game_over():
return self.evaluate_position(board), None
best_move = None
if maximizing_player:
max_eval = float('-inf')
for move in board.legal_moves:
board.push(move)
eval, _ = self.minimax(board, depth - 1, False)
board.pop()
if eval > max_eval:
max_eval = eval
best_move = move
return max_eval, best_move
else:
min_eval = float('inf')
for move in board.legal_moves:
board.push(move)
eval, _ = self.minimax(board, depth - 1, True)
board.pop()
if eval < min_eval:
min_eval = eval
best_move = move
return min_eval, best_move
def get_move(self, board):
"""
Main method to select the best move.
"""
, bestmove = self.minimax(board, depth=3,
maximizing_player=board.turn)
return best_move
## Understanding the Code
Let's break down how the minimax implementation works:
1. Position Evaluation (`evaluate_position`)
- Checks if the game is over:
- Returns 10000 for checkmate (positive if white wins, negative if black wins)
- Returns 0 for draws
- Calculates material score using standard piece values:
- Pawns = 100 points
- Knights = 320 points
- Bishops = 330 points (slightly better than knights)
- Rooks = 500 points
- Queens = 900 points
- Kings = 20000 points (effectively infinite)
- Adds points for white pieces, subtracts for black pieces
- Current implementation only considers material - we'll improve this later!
2. Minimax Algorithm (`minimax`)
- Takes three parameters:
- board: Current chess position
- depth: How many moves ahead to look
- maximizing_player: Whether current player is maximizing (white) or minimizing (black)
- Base cases:
- If depth = 0: Stop and evaluate position
- If game is over: Return the result
- For maximizing player (white):
- Try each legal move
- Recursively evaluate opponent's best response
- Keep track of highest evaluation found
- Remember which move led to best position
- For minimizing player (black):
- Same process but keeps lowest evaluation
- Returns both the evaluation and the best move found
3. Move Selection (`get_move`)
- Entry point for the bot
- Calls minimax with depth 3 (looks 3 moves ahead)
- Returns the best move found
While our current implementation works, it has a serious efficiency problem. Let's consider the numbers:
- Average chess position has about 30 legal moves
- Looking 3 moves ahead means examining:
- Your 30 moves
- Opponent's 30 responses to each (900 positions)
- Your 30 responses to each of those (27,000 positions)
- Total positions = 30 30 30 = 27,000
What if we want to look 4 moves ahead? That becomes 810,000 positions!
5 moves ahead? 24.3 million positions!
6 moves ahead? 729 million positions!
This exponential growth makes deeper search practically impossible. A strong chess engine needs to look at least 6-8 moves ahead to play well. With our current implementation, that would take hours per move!
This is where alpha-beta pruning comes in. It's not a different algorithm - it's an optimization of minimax that lets us skip analyzing moves that we can prove won't affect our final decision.
The key insight is that once we find a good move, we can use that information to avoid analyzing clearly worse moves.
Imagine you're playing chess and thinking ahead. You're analyzing a move and find that it leads to a terrible position. Would you keep analyzing other variations of that move? Of course not! Alpha-beta pruning formalizes this intuition.
Let's walk through an example:
1. Alpha (α): Represents the minimum score that the maximizing player is assured of
2. Beta (β): Represents the maximum score that the minimizing player is assured of
Think of it like this:
- You're searching through a tree of moves
- You find a good move that gives you a score of 5
- Later, you're analyzing another move
- After a few variations, you realize your opponent can force a position with a score of 3
- Since you already have a move that guarantees 5, why continue analyzing this worse position?
- This is a "cutoff" - you can skip analyzing the rest of this branch
Let's say you're analyzing two moves:
1. Queen takes pawn, checking the king
2. Knight fork attacking queen and rook
While analyzing the queen takes pawn line:
- You see your opponent has only one legal move (block or move king)
- This leads to a position where you're up material
- The minimum score you'll get is +2 (α = 2)
Now analyzing the knight fork:
- First variation shows you win a queen (+9)
- Second variation shows you win a rook (+5)
- Third variation... wait! Your opponent can force a position worse than +2
- No need to analyze further - you already know the queen takes pawn line is better
1. Massive Performance Improvement
- Can reduce the number of positions evaluated by 50-90%
- Allows searching much deeper in the same amount of time
- More efficient move ordering leads to more cutoffs
2. Move Ordering
- The effectiveness of alpha-beta pruning depends heavily on move ordering
- Check captures first
- Then threats
- Then positionally strong moves
1. Implement the basic minimax algorithm provided
2. Add position evaluation function
3. Test different search depths (start with 3)
4. Think about move ordering:
- List what moves should be checked first
- Plan how you would implement this ordering
5. Design your alpha-beta pruning implementation and implement it in your code
* [Chess Programming Wiki - Alpha-Beta](https://www.chessprogramming.org/Alpha-Beta)
* [Move Ordering Techniques](https://www.chessprogramming.org/Move_Ordering)
* [Principal Variation Search](https://www.chessprogramming.org/Principal_Variation_Search)
Remember to test your bot frequently and analyze its games. Pay attention to positions where it makes mistakes - these will help you tune your evaluation function.
Good luck, and let us know if you need any help implementing these concepts!
